Square + triangle = sine (almost)
in [Design]
|
Prev: Avalanche Photodetector
Next: Cheap potting alternative
From: MooseFET on 10 Mar 2010 01:41 On Mar 9, 9:38 pm, "JosephKK"<quiettechb...(a)yahoo.com> wrote: > On Tue, 9 Mar 2010 06:35:44 -0800 (PST), MooseFET <kensm...(a)rahul.net> wrote: > >On Mar 9, 12:22 am, Fred Bartoli <myname_with_a_dot_inbetw...(a)free.fr> > >wrote: > >> MooseFET a écrit : > > >> > On Mar 8, 8:28 am, "Tim Williams" <tmoran...(a)charter.net> wrote: > >> >> "MooseFET" <kensm...(a)rahul.net> wrote in message > > >> >>news:c968f0a3-64bc-46e1-8a14-7b36a8e75d0f(a)b9g2000pri.googlegroups.com... > > >> >>> If you use a quad comparator, you can do some interesting stuff. With > >> >>> just 2 more comparators, you can make this: > >> >>> ------ ------ > >> >>> --- --- --- --- > >> >>> ------ > >> >> I recollect something from Don Lancaster about Magic Sinewaves and how you > >> >> can get arbitrarily low harmonics from certain optimal patterns of on and > >> >> off, given sufficiently accurate timing, and I suppose some sort of > >> >> filtering. I never did figure out if it's supposed to be a tristate > >> >> waveform (as above) > > >> > The waveform I drew can be made by simply adding two pulse trains > >> > with > >> > different duty cycles. The fact that 3 time 60 degrees is 180 degrees > >> > is how you can get the 3rd harmonic to go away. > > >> > If you use more steps, you can get the first N harmonics to drop to > >> > zero. The same is true for line segments instead of steps. > > >> Which is nothing more than the analog variant of a transversal filter > >> that you can build from a divider, a shift register and a few weighted > >> summing resistors. > > >It is the same idea but in this case, it is made from a triangle wave > >which we have to start with instead of needing to make a higher > >frequency > >first. > > >> -- > >> Thanks, > >> Fred. > > Just to be off the wall, what is the integral of a triangle wave? > How about the second and third integrals? Each time you integrate, the segment between switching points becomes a higher power of X. Square wave X^0 Triangle wave X^1 ?????? wave X^2 Cubic wave X^3
From: Don Klipstein on 10 Mar 2010 01:43 In article <AvOdnWKo1Yb_vwrWnZ2dnUVZ_u6dnZ2d(a)earthlink.com>, Bitrex wrote: >Jim Thompson wrote: <SNIP to here> >> Ah, yes! Thanks for the reminder! I also linearized a frequency >> hopping VCO for OmniSpectra _many_ years ago... for jumping close to >> desired frequency, so the PLL lock was faster... a cavity beast :-) >> >> I would never use _just_ diodes, rather use them with OpAmps or >> comparators, such as... >> >> http://analog-innovations.com/SED/ClampForLarkin.pdf >> >> (A Christmas gift, 2007. But he remains a cranky old git :-) >> >> http://analog-innovations.com/SED/LevelDetectAndFollow-LM339.pdf >> >> http://analog-innovations.com/SED/LevelDetectAndFollow-TL431.pdf >> >> http://analog-innovations.com/SED/PerfectDiodeForChargerIsolation.pdf >> >> ...Jim Thompson > >The first schematic looks like the start of a decent guitar fuzzbox >pedal! I think one could set more breakpoints with different slopes by >using more comparators with the breakpoint voltage on the non inverting >inputs and putting resistors in series with the diodes, right? > >Back before guitar practice amps with DSP became commodity hardware, >Peavey had a patented technology called "TransTube" that purported to >make a solid state amp have a tone more like a tube amp. I wonder if >they used a similar piecewise linear technique to make the amp have a >softer clipping characteristic. A little over a decade ago, I worked along with 2 partners on what we hoped would be a patentable significant on an "electric guitar fuzzbox". As in able to get a patent for improvement over prior art in US patents by Pittman and Scholz (sp). "Our" device received rave reviews where we showed it off. "We" abandoned the project after determining that "we" could make a majority as much money working at entry level at a big-name fast-food restaurant as "we" could getting this device manufactured and selling it, even should (unlikely) sales volume get the cost of patenting it to be negligible-per-unit, let alone battling whoever tries their hand at infringing "our patent" in a case likely costing upper 10's of kilobucks to hundreds of kilobucks (I can't rule out megabucks) in a court battle. One of "us" (we 3) even schmoozed the likely examiner of the prospective patent application to extent of hearing from the likely examiner that a patent would likely be granted. This "improved fuzzbox" never went to any actually filed patent application. It was since published on the web, at least significantly where web searching for it or major segments of it are best found by AND-ing search terms of "LXH2" and either of the 2 major brands of British electric guitar amplifiers - Fender or Marshall. - Don Klipstein (don(a)misty.com)
From: Robert Baer on 10 Mar 2010 01:46 Jim Thompson wrote: > On Mon, 08 Mar 2010 21:42:22 -0800, > "JosephKK"<quiettechblue(a)yahoo.com> wrote: > >> On Mon, 08 Mar 2010 09:25:15 -0700, Jim Thompson <To-Email-Use-The-Envelope-Icon(a)My-Web-Site.com> wrote: >> >>> On Mon, 08 Mar 2010 00:01:44 -0800, Muzaffer Kal <kal(a)dspia.com> >>> wrote: >>> >>>> On Sun, 07 Mar 2010 23:11:20 -0800, >>>> "JosephKK"<quiettechblue(a)yahoo.com> wrote: >>>> >>>>> On Sat, 6 Mar 2010 20:21:10 -0800, D from BC <myrealaddress(a)comic.com> wrote: >>>>> >>>>>> In article <4b9324ee.4432562(a)news.tpg.com.au>, rontanner(a)esterbrook.com >>>>>> says... >>>>>>> On Sun, 7 Mar 2010 14:31:48 +1100, "Phil Allison" <phil_a(a)tpg.com.au> >>>>>>> wrote: >>>>>>> >>>>>>>> "Harold Larsen" >>>>>>>>> If a squarewave contains all odd harmonics of the fundamental >>>>>>>>> frequency, and a triangle all even, >>>>>>>> >>>>>>>> ** Sorry - that is WRONG . >>>>>>>> >>>>>>>> A triangle wave contains only odd harmonics too. >>>>>>>> >>>>>>>> http://en.wikipedia.org/wiki/Triangle_wave >>>>>>>> >>>>>>>> A "sawtooth" wave contains all integer harmonics. >>>>>>>> >>>>>>> OK thanks for the pull-up, but how about using a triangle-square wave >>>>>>> mix, in place of a filter, to simulate a sinewave . >>>>>>> >>>>>>> I have not seen that method applied or described anywhere, but it >>>>>>> makes a fair approximation, at least to my eye. >>>>>>> >>>>>>> Harold Larsen >>>>>> >>>>>> This reminds of the XR2206 chip that makes square, triangle and sine >>>>>> using analog technology. >>>>> Sure enough, as does the ICL8038. Part of the question is how it is done. >>>> The datasheet at http://www.intersil.com/data/FN/FN2864.pdf has a >>>> pretty good schematic and explanation which shows how it's done. >>> Yep. "Piecewise-Linear", aka break-point analysis... taught in better >>> engineering schools ;-) >>> >>> ...Jim Thompson >> I first saw it in a synchro to digital converter about 1973. I had to think >> hard for a while before i "got" it. > > The only place I can remember using it in an actual product was for > linearizing a flat-face CRT sweep (RADAR)... and there it was > piecewise _curve_ fitting. > > ...Jim Thompson Yup! Good 'ole analog DFGs..
From: Don Klipstein on 10 Mar 2010 02:04 In art. <a1cep55fuh2dlo9lc0k9jeu1d1rsp9btaf(a)4ax.com>, JosephKK wrote: <SNIP a lot of previously quoted material> >Just to be off the wall, what is the integral of a triangle wave? >How about the second and third integrals? Integral of a triangle wave is a "nearly-sinusoid" having periodic parabolic arches. This reminds me of a story... During my 2nd (and successful) attempt to pass "Electronic Instrumentation Laboratory" course at Drexel U. around 1983-1984 or so, I had to handle the 10th of 10 weekly "laboratory projects". That was an "analog computer" that modelled a damped resonant item such as a "damped pendulum". This used a circuit having two op-amp integrators with arrangement so as to model K1 * y'' + K2 * y' plus K3 * y = zero. I was one of only 2 out of 78-or-so students taking that course that semester who managed to make this thing work. (Not that I did so well or better most of elsewhere in my attempt for an EE degree...) I got the circuit to work by recognizing a "parabola arch wave" on an oscilloscope to be visibly discernable from a sinusoid, and subsequently setting "initial conditions" short of any of the op-amps clipping. (The parabolic arch waveform was due to a heavily clipped sinusoid being integrated twice.) Fixing the clipping issue achieved the oscillation damping-out rather than growing. - Don Klipstein (Jr) don(a)misty.com
From: Bitrex on 10 Mar 2010 04:50
MooseFET wrote: > On Mar 9, 8:36 pm, Bitrex <bit...(a)de.lete.earthlink.net> wrote: >> Jim Thompson wrote: >>> On Tue, 09 Mar 2010 10:10:26 -0500, Phil Hobbs >>> <pcdhSpamMeSensel...(a)electrooptical.net> wrote: >>>> On 3/9/2010 9:59 AM, Jim Thompson wrote: >>>>> On Mon, 08 Mar 2010 21:42:22 -0800, >>>>> "JosephKK"<quiettechb...(a)yahoo.com> wrote: >>>>>> On Mon, 08 Mar 2010 09:25:15 -0700, Jim Thompson<To-Email-Use-The-Envelope-I...(a)My-Web-Site.com> wrote: >>>>>>> On Mon, 08 Mar 2010 00:01:44 -0800, Muzaffer Kal<k...(a)dspia.com> >>>>>>> wrote: >>>>>>>> On Sun, 07 Mar 2010 23:11:20 -0800, >>>>>>>> "JosephKK"<quiettechb...(a)yahoo.com> wrote: >>>>>>>>> On Sat, 6 Mar 2010 20:21:10 -0800, D from BC<myrealaddr...(a)comic.com> wrote: >>>>>>>>>> In article<4b9324ee.4432...(a)news.tpg.com.au>, rontan...(a)esterbrook.com >>>>>>>>>> says... >>>>>>>>>>> On Sun, 7 Mar 2010 14:31:48 +1100, "Phil Allison"<phi...(a)tpg.com.au> >>>>>>>>>>> wrote: >>>>>>>>>>>> "Harold Larsen" >>>>>>>>>>>>> If a squarewave contains all odd harmonics of the fundamental >>>>>>>>>>>>> frequency, and a triangle all even, >>>>>>>>>>>> ** Sorry - that is WRONG . >>>>>>>>>>>> A triangle wave contains only odd harmonics too. >>>>>>>>>>>> http://en.wikipedia.org/wiki/Triangle_wave >>>>>>>>>>>> A "sawtooth" wave contains all integer harmonics. >>>>>>>>>>> OK thanks for the pull-up, but how about using a triangle-square wave >>>>>>>>>>> mix, in place of a filter, to simulate a sinewave . >>>>>>>>>>> I have not seen that method applied or described anywhere, but it >>>>>>>>>>> makes a fair approximation, at least to my eye. >>>>>>>>>>> Harold Larsen >>>>>>>>>> This reminds of the XR2206 chip that makes square, triangle and sine >>>>>>>>>> using analog technology. >>>>>>>>> Sure enough, as does the ICL8038. Part of the question is how it is done. >>>>>>>> The datasheet athttp://www.intersil.com/data/FN/FN2864.pdfhas a >>>>>>>> pretty good schematic and explanation which shows how it's done. >>>>>>> Yep. "Piecewise-Linear", aka break-point analysis... taught in better >>>>>>> engineering schools ;-) >>>>>>> ...Jim Thompson >>>>>> I first saw it in a synchro to digital converter about 1973. I had to think >>>>>> hard for a while before i "got" it. >>>>> The only place I can remember using it in an actual product was for >>>>> linearizing a flat-face CRT sweep (RADAR)... and there it was >>>>> piecewise _curve_ fitting. >>>>> ...Jim Thompson >>>> Breakpoint amps are nearly always a crutch. One poor guy I tried to >>>> help (15 years back) ignored my advice and wound up with a multi-diode >>>> breakpoint amp stuck inside a crystal oven to keep the breakpoints from >>>> going all over the place with temperature. Blech. (It was in a fancy >>>> measurement system, too. Got all sorts of industry awards.) >>>> The Widlar approach (National AN4, Figure 8) uses BJT saturation to make >>>> nice sharp breakpoints that don't drift much. Of course you have to >>>> wait for the transistor to come out of saturation. >>>> About the only good use of breakpoint amps I've seen is inside >>>> complicated FB loops, e.g. to approximately correct for the nonlinearity >>>> of VCOs and heaters. This reduces the variation of loop gain and so >>>> makes frequency compensation easier. Drift and inaccuracy are not a big >>>> problem in those sorts of applications. >>>> Cheers >>>> Phil Hobbs >>> Ah, yes! Thanks for the reminder! I also linearized a frequency >>> hopping VCO for OmniSpectra _many_ years ago... for jumping close to >>> desired frequency, so the PLL lock was faster... a cavity beast :-) >>> I would never use _just_ diodes, rather use them with OpAmps or >>> comparators, such as... >>> http://analog-innovations.com/SED/ClampForLarkin.pdf >>> (A Christmas gift, 2007. But he remains a cranky old git :-) >>> http://analog-innovations.com/SED/LevelDetectAndFollow-LM339.pdf >>> http://analog-innovations.com/SED/LevelDetectAndFollow-TL431.pdf >>> http://analog-innovations.com/SED/PerfectDiodeForChargerIsolation.pdf >>> ...Jim Thompson >> The first schematic looks like the start of a decent guitar fuzzbox >> pedal! I think one could set more breakpoints with different slopes by >> using more comparators with the breakpoint voltage on the non inverting >> inputs and putting resistors in series with the diodes, right? >> >> Back before guitar practice amps with DSP became commodity hardware, >> Peavey had a patented technology called "TransTube" that purported to >> make a solid state amp have a tone more like a tube amp. I wonder if >> they used a similar piecewise linear technique to make the amp have a >> softer clipping characteristic. > > At lowish frequencies, you can do this: > > ---------------------------------------/\/\---+----Out > ! ! > +-----------------/\/\----+-/\/\---+---/\/\----+ > ! ! ! ! > ! --!-\ ! ! > In ---+--------!+\ ! >-- ! > ! >---+--/\/\--+---!+/ ! > --!-/ ! ! ! > ! ! ---/\/\--GND ! > GND--/\/\--+--/\/\---+------------------------/\/\-- > > With rail to rail op-amps, you can get a total of 6 knees from Vee to > Vcc in the output > swing. I'm having trouble following that circuit - it looks clever, but how does it work? |